In the construction of complex cryptocurrency systems with infinite parallel computing capabilities and high adaptability, the asymmetric P/NP interaction model plays a critical role. This article begins with the parallelization needs of distributed account systems, delves into the key role of the P/NP model in transaction execution, and uses Bitcoin as an example to illustrate how it leverages this model to achieve adaptability and concurrency.
Traditional centralized account systems function like atomic execution units governed by a single world state tree, where all account operations must be executed serially. This inherent sequential nature severely limits system throughput and makes it difficult to accommodate the demands of large-scale concurrent transactions.
To break through this bottleneck, distributed account systems emerged. In this model, each account operates as an independent atomic execution unit with its own attributes and state. This design allows operations related to different accounts to be executed in parallel, theoretically enabling infinite concurrency.
Building a truly decentralized distributed account system hinges on ensuring the independence of each account and the uniqueness of ownership. Asymmetric cryptographic technology plays a core role here. By mapping each account’s attributes and state to keys generated through asymmetric elliptic curve cryptography, the atomicity between the key and the account system can be ensured. The holder of the private key can independently control the account and initiate transactions without centralized coordination, laying the groundwork for parallel processing.
Building on the atomicity of distributed account systems, the key to achieving infinite parallelism and adaptive energy efficiency lies in the asymmetric P/NP model of transaction execution. This model treats the process of transaction construction as a computationally hard NP (Non-deterministic Polynomial time) problem, while the transaction validation process is treated as a P (Polynomial time) problem that can be completed within polynomial time.
In practical implementation, individuals with access to the private key of an account are solely responsible for independently constructing transactions (NP solving)—creating transactions based on personal intent and account state, including specifying inputs, outputs, and signatures. This process is executed entirely locally by the user, without involvement from other nodes in the network.
The constructed transaction is then submitted to a notary system (e.g., the blockchain) for validation. The validation process (a P problem) is relatively simple and efficient, mainly involving checks on the validity of the signature, whether the input UTXO has already been spent, and whether the transaction structure conforms to protocol rules. Since validation is quick, the notary system can efficiently handle a large volume of concurrent transaction verification requests.
This asymmetric P/NP design brings significant advantages:
Bitcoin’s success as the first decentralized cryptocurrency with potential for infinite concurrency and adaptability is largely due to its clever application of the asymmetric P/NP model.
Bitcoin’s UTXO (Unspent Transaction Output) model is a classic representation of a distributed account system. Each UTXO is mapped to one or more asymmetric cryptographic keys, forming an independent and indivisible atomic unit. Ownership of a UTXO is entirely controlled by the corresponding private key.
Bitcoin’s transaction construction process perfectly embodies the asymmetric P/NP model:
Furthermore, Bitcoin’s Lightning Network, as an extension solution for BTC payments, further deepens the application of the asymmetric P/NP model. The Lightning Network establishes off-chain state channels between participants, allowing multiple rapid and low-cost transactions, with interaction with the main chain only occurring during channel opening and closing. Validation of off-chain transactions is more lightweight, significantly improving transaction concurrency and efficiency.
The asymmetric P/NP interaction model is a core design principle for building complex adaptive cryptocurrency systems. By combining distributed account systems with asymmetric cryptographic technology, and cleverly separating the transaction construction and validation processes into NP and P problems, such systems can achieve high parallel processing capacity, avoid redundant computation, and lay a foundation for future adaptive optimization. Bitcoin’s success is a powerful testament to the vitality of this model. A deep understanding and application of this model will be key to future advancements and innovations in cryptocurrency technologies.
